Said needles are known to usually comprise a pointed metal tube joined to a hollow support member which is fixed to the cylindrical body of the syringe. The present invention confronts the problem of protection against pricking by needles especially after they have been inserted into a patient's body. In this respect, if needles prick or scratch a second person after they have been used on a first person, they can become a transmission vehicle for diseases. There is therefore a considerable danger connected with the handling of these needles especially by those who usually work with them, in particular hospital staff. The disposal of used needles as refuse also creates danger for those who handle the refuse containers or who approach such containers. For these reasons it has become usual, after their use, to cover the point of such needles by remounting on them the cap which is used to protect the needle before use. However, mounting said cap on the needle is an operation which requires a certain precision and has also resulted in pricking. A further drawback is that when the cap is removed from the needle it can easily become lost, being of relatively small dimensions.